Quantum thermalization of long-range interacting spins*

Our goal is to define under which condition a long-range interacting quantum many-body system set out of equilibrium relaxes under the effect of interactions between its constituents.

For this, we investigate the spin dynamics and quantum thermalization of a macroscopic ensemble of S = 3 spins initially prepared in a pure coherent spin state. The experiment uses a unit-filled array of 10 thousand chromium atoms in a three dimensional optical lattice. Atoms interact at long distance under the effect of magnetic dipole-dipole interactions, realizing the spin-3 XXZ Heisenberg model with long-range couplings.

We quench this system in an out-of-equilibrium situation by tilting the spins with respect to the magnetic field, and study its evolution by measuring global properties, such as the total population in the seven different Zeeman states or the collective spin length. We find that these observables rapidly relax towards an equilibrium state, in good agreement with the quantum thermalization scenario and the eigenstate thermalization hypothesis. We also find that the measurement of magnetization fluctuations provides direct quantitative estimates for two-body correlations that increase under the effect of interactions.

On the other hand, when the experiment is performed in the BEC phase, without a lattice, the system is well described by hydrodynamic equations, and a long-lived trapped magnon mode is created, showing no sign of thermalization at the experimental timescale.